Suppose you are trying to assess whether or not the GPAs of 52 students in an honors seminar course are greater than 3.5. The 52 seminar stu

Question

Suppose you are trying to assess whether or not the GPAs of 52 students in an honors seminar course are greater than 3.5. The 52 seminar students have a mean GPA of 3.55, with a standard deviation of 0.2. Which of the following corresponds to the p-value for this test?
a) p 0.0211
b) p 0.0053
c) p 0.9947
d) p 0.964
e) p 0.0357
f) p 0.053
g) p 1.803

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Reagan 2 weeks 2021-09-11T00:38:42+00:00 1 Answer 0

Answers ( )

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    2021-09-11T00:39:50+00:00

    Answer:

    t=\frac{3.55-3.5}{\frac{0.2}{\sqrt{52}}}=1.80    

    The degrees of freedom are given by:

    df=n-1=52-1=51  

    The p value for this case can be calculated on this way:

    p_v =P(t_{(51)}>1.80)=0.036  

    And the most appropiate value for this case would be :

    e) p= 0.0357

    Step-by-step explanation:

    Information given

    \bar X=3.55 represent the sample mean for the GPA

    s=0.2 represent the sample standard deviation

    n=52 sample size  

    \mu_o =3.5 represent the value that we want to test

    t would represent the statistic

    p_v represent the p value

    System of hypothesis

    We need want to verify if students in an honors seminar course are greater than 3.5, the system of hypothesis would be:  

    Null hypothesis:\mu \leq 3.5  

    Alternative hypothesis:\mu > 3.5  

    The statistic is given by:

    t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

    Replacing the info given we got:

    t=\frac{3.55-3.5}{\frac{0.2}{\sqrt{52}}}=1.80    

    The degrees of freedom are given by:

    df=n-1=52-1=51  

    The p value for this case can be calculated on this way:

    p_v =P(t_{(51)}>1.80)=0.036  

    And the most appropiate value for this case would be :

    e) p= 0.0357

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